Closing a hole after adding solidify modifier
Can you post screenshots of your mesh without modifiers? It's hard to tell from the images, but it looks like you have a non-manifold mesh, that is a mesh that could not exist or be built in real life.

In your case it seems you have edges that belong to more than two faces. Specifically that large circular "lid" that makes inner part of the lamp is probably attached to the outer faces causing an inconsistency in your mesh that the solidify modifier can't handle correctly.

I would advise choosing one of the two methods and sticking with it.

If you require modeling the inside of the mesh than abandon the modifiers completely and model it all the way through.

I always prefer a modifiers non destructive workflow so in your case you could either detach the "lid" into a separate object that doesn't use a solidify modifier, or leave it in the same mesh but detach it from the surrounding geometry, making it a separate chunk.

Edit: As I mentioned previously, closing the mesh at the selected loop will yield a non manifold mesh, you would be creating a an inner face that would be connected to the outer part of the shell.
I mean, you can do it, but it will generate a mesh that will most likely cause problems with most modifiers and create a topology that is troublesome.

The way I see it you have four choices:


Apply the solidify, enter edit mode select the inner center vertex, grow the selection with Ctrl + + until the desired loops are selected and X > dissolve faces.
Drop the solidify modifier or and manually model the interior with the closed loop as desired. There is an edit mode Solidify operator you can use.
Leave the solidfy modifier, duplicate the selected loop with Shift + D then press F to close it. It will create a separate chunk of mesh and a discontinuity in the object, but it will remain a manifold watertight object and leave the modifier in place.
My favorite would be to rethink the whole object and use a screw modifier instead. Just draw the section of the light bulb and then use a Screw Modifier.